Spin Hall magnetoresistance in a low-dimensional Heisenberg ferromagnet

We report the spin Hall magnetoresistance (SMR) in Pt deposited on a tensile-strained LaCoO₃ (LCO) thin film, which is a ferromagnetic insulator with a Curie temperature T₂=850. 28em{0ex}K. The SMR displays a strong magnetic-field dependence below T₂, with the SMR amplitude continuing to increase (linearly) with increasing the field far beyond the saturation value of the ferromagnet. The SMR amplitude decreases gradually with raising the temperature across T₂ and remains measurable even above T₂. Moreover, no hysteresis is observed in the field dependence of the SMR. These unusual behaviors indicate that a low-dimensional magnetic system forms at the surface of LCO and that the LCO/Pt interface decouples magnetically from the rest of the LCO thin film. Transmission electron microscopy analysis of the heterostructure reveals that an ultrathin Co-rich layer forms at the LCO surface upon deposition of Pt, which is separated from the rest of the LCO film by a 1-nm La/O-rich layer, thus supporting the presence of a low-dimensional ferromagnetic system. To explain the magnetoresistance measurements, we revisit the derivation of the SMR corrections and relate the spin-mixing conductances to the spin-spin correlation functions and microscopic quantities describing the magnetism at the interface. Comparisons between theory and experiment confirm the existence of a low-dimensional Heisenberg ferromagnet at the interface. Our results pave the way for exploring complex magnetic textures of insulating films by simple transport measurements.